Cash or card to pay with?

Nearly four years ago, in my old blog, I mentioned the design of self-service checkouts at supermarkets. (See <a href="http://iaoreditor.blogspot.co.uk/2009/03/coin-machine-problem.html">this</a>.) In Exeter we have a new twist to the design of supermarket self-service checkouts, and I was pondering the modelling that has gone into the design of this system.

In our local Waitrose supermarket, there are several conventional checkouts, which are staffed according to demand. One or two further ones are open to customers with one basket. A third option is to take a scanner which you use as you go round the store, and then pay at a checkout dedicated to such machines. It is the fourth option whose modelling I was thinking about. Here are three self-service tills, but the only way to pay is by card, either credit or debit.

So, the modelling has come up with the need for these machines (as opposed to ones taking coins) and for three of these machines. On what basis?

First, the space constraint. These three fit into a similar space to that occupied by a conventional checkout. So, the choice is between three and six.

Second, the capital cost. Presumably, machines which do not need coins are cheaper to make.

Third, the day-to-day running cost. These machines do not need to be refilled with coins, and because they do not have the mechanical parts for coin collection and return, are less likely to break down.

Fourth, the financial running cost. The supermarket pays fees for card transactions, so the modelling must include these. Against this, the supermarket would be paying for cash transactions at its bank, so is saving these charges.

Fifth, human behaviour. Presumably, like other stores, the supermarket has collected data about the number of card transactions and the distribution of the size of these, and also the number of cash transactions and the distribution of their size. Since the store is part of a national chain, there will be data about these transactions on such machines where they had been introduced before our local store opened.

What I would find particularly interesting is to know the extent to which the presence of these machines has changed human behaviour. There are several types of customer to consider. Some people will pay by card at any type of check-out, irrespective of the total amount of the purchase. (I am almost in that category, though I do use cash on self-service machines from time to time for very small purchases. It may be inconsistent, but I don't use a card when making small purchases with independent traders, who generally pay a higher charge for card transactions than do the multi-branch supermarkets.) Some people will use a check-out with a human cashier every time they shop. Some people will decide which check-out to use depending on the amount purchased (self-service tills have a small area for packing bags, and a conventional till has advantages in such cases). But there must be a category of shopper whose behaviour has been modified by these card-only machines. How many people are willing to use a self-service machine, would prefer to pay by cash when they did so, but change to a card in this situation?

And having asked the questions, I wonder how they collected the data. And do the statistics change with time, either as a trend or with seasonality?

Once again, I realise that you need to include psychology of behaviour in the mathematical and financial OR model.

Yes, I should have mentioned that possibility too -- all part of the psychology of customers in supermarkets. There is also the possibility that some card-using customers will decide "which way to go" when they see the queues at different types of check-out.